JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 July 2022, Shift 2, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

\alpha,\beta\ (\alpha>\beta)

be the roots of the quadratic equation

x^2-x-4=0

. If

P_n=\alpha^n-\beta^n

n\in\mathbb{N}

, then

\frac{P_{15}P_{16}-P_{14}P_{16}-P_{15}^2+P_{14}P_{15}}{P_{13}P_{14}}

is equal to ________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Newton's Sums

Same idea in other shifts

Asked 16× in all

6 Apr 2026, Shift 2 · Q3Let $S=\{z\in\mathbb{C}: z^2+\sqrt{6}\,iz-3=0\}$ . Then $\sum_{z\in S} z^8$ is equal to :MediumSingle correct
2 Apr 2025, Shift 1 · Q17Let $P_n=\alpha^n+\beta^n$ , $n\in\mathbf{N}$ . If $P_{10}=123$ , $P_9=76$ , $P_8=47$ and $P_1=1$ , then the quadratic equation having roots…MediumSingle correct
3 Apr 2025, Shift 1 · Q3Let $\alpha$ and $\beta$ be the roots of $x^2 + \sqrt{3}x - 16 = 0$ , and $\gamma$ and $\delta$ be the roots of $x^2 + 3x - 1 = 0$ . If…MediumSingle correct
6 Apr 2024, Shift 1 · Q4Let $\alpha, \beta$ be the distinct roots of the equation $x^2-(t^2-5t+6)x+1=0$ , $t \in \mathbb{R}$ and $a_n=\alpha^n+\beta^n$ . Then the…HardSingle correct
6 Apr 2024, Shift 2 · Q21Let $\alpha,\beta$ be roots of $x^2+\sqrt{2}x-8=0$ . If $U_n=\alpha^n+\beta^n$ , then $\frac{U_{10}+\sqrt{2}U_9}{2U_8}$ is equal to ________.EasyNumerical value
9 Apr 2024, Shift 2 · Q3Let $\alpha, \beta;\ \alpha>\beta$ , be the roots of the equation $x^2-\sqrt{2}x-\sqrt{3}=0$ . Let $P_n=\alpha^n-\beta^n,\ n\in\mathbb{N}$ .…MediumSingle correct
11 Apr 2023, Shift 1 · Q24If $a$ and $b$ are the roots of the equation $x^2 - 7x - 1 = 0$ , then the value of…MediumNumerical value
12 Apr 2023, Shift 1 · Q2Let $\alpha, \beta$ be the roots of the quadratic equation $x^2+\sqrt{6}x+3=0$ . Then…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.